Reduced feedback for beamforming in a wireless communication

ABSTRACT

A method for reduced feedback for beamforming in a wireless communication begins by receiving a baseband signal. The method continues by digitally beamforming the baseband signal using a unitary matrix having polar coordinates.

CROSS REFERENCE TO RELATED PATENTS

This invention is claiming priority under 35 USC §119(e) to aprovisionally filed patent application having the same title as thepresent patent application, a filing date of Apr. 21, 2005, and anapplication No. 60/673,451.

BACKGROUND OF THE INVENTION

1. Technical Field of the Invention

This invention relates generally to wireless communication systems andmore particularly to wireless communications using beamforming.

2. Description of Related Art

Communication systems are known to support wireless and wire linedcommunications between wireless and/or wire lined communication devices.Such communication systems range from national and/or internationalcellular telephone systems to the Internet to point-to-point in-homewireless networks. Each type of communication system is constructed, andhence operates, in accordance with one or more communication standards.For instance, wireless communication systems may operate in accordancewith one or more standards including, but not limited to, IEEE 802.11,Bluetooth, advanced mobile phone services (AMPS), digital AMPS, globalsystem for mobile communications (GSM), code division multiple access(CDMA), local multi-point distribution systems (LMDS),multi-channel-multi-point distribution systems (MMDS), and/or variationsthereof.

Depending on the type of wireless communication system, a wirelesscommunication device, such as a cellular telephone, two-way radio,personal digital assistant (PDA), personal computer (PC), laptopcomputer, home entertainment equipment, et cetera communicates directlyor indirectly with other wireless communication devices. For directcommunications (also known as point-to-point communications), theparticipating wireless communication devices tune their receivers andtransmitters to the same channel or channels (e.g., one of the pluralityof radio frequency (RF) carriers of the wireless communication system)and communicate over that channel(s). For indirect wirelesscommunications, each wireless communication device communicates directlywith an associated base station (e.g., for cellular services) and/or anassociated access point (e.g., for an in-home or in-building wirelessnetwork) via an assigned channel. To complete a communication connectionbetween the wireless communication devices, the associated base stationsand/or associated access points communicate with each other directly,via a system controller, via the public switch telephone network, viathe Internet, and/or via some other wide area network.

For each wireless communication device to participate in wirelesscommunications, it includes a built-in radio transceiver (i.e., receiverand transmitter) or is coupled to an associated radio transceiver (e.g.,a station for in-home and/or in-building wireless communicationnetworks, RF modem, etc.). As is known, the receiver is coupled to theantenna and includes a low noise amplifier, one or more intermediatefrequency stages, a filtering stage, and a data recovery stage. The lownoise amplifier receives inbound RF signals via the antenna andamplifies then. The one or more intermediate frequency stages mix theamplified RF signals with one or more local oscillations to convert theamplified RF signal into baseband signals or intermediate frequency (IF)signals. The filtering stage filters the baseband signals or the IFsignals to attenuate unwanted out of band signals to produce filteredsignals. The data recovery stage recovers raw data from the filteredsignals in accordance with the particular wireless communicationstandard.

As is also known, the transmitter includes a data modulation stage, oneor more intermediate frequency stages, and a power amplifier. The datamodulation stage converts raw data into baseband signals in accordancewith a particular wireless communication standard. The one or moreintermediate frequency stages mix the baseband signals with one or morelocal oscillations to produce RF signals. The power amplifier amplifiesthe RF signals prior to transmission via an antenna.

In many systems, the transmitter will include one antenna fortransmitting the RF signals, which are received by a single antenna, ormultiple antennas, of a receiver. When the receiver includes two or moreantennas, the receiver will select one of them to receive the incomingRF signals. In this instance, the wireless communication between thetransmitter and receiver is a single-output-single-input (SISO)communication, even if the receiver includes multiple antennas that areused as diversity antennas (i.e., selecting one of them to receive theincoming RF signals). For SISO wireless communications, a transceiverincludes one transmitter and one receiver. Currently, most wirelesslocal area networks (WLAN) that are IEEE 802.11, 802.11a, 802.11b, or802.11g employ SISO wireless communications.

Other types of wireless communications includesingle-input-multiple-output (SIMO), multiple-input-single-output(MISO), and multiple-input-multiple-output (MIMO). In a SIMO wirelesscommunication, a single transmitter processes data into radio frequencysignals that are transmitted to a receiver. The receiver includes two ormore antennas and two or more receiver paths. Each of the antennasreceives the RF signals and provides them to a corresponding receiverpath (e.g., LNA, down conversion module, filters, and ADCs). Each of thereceiver paths processes the received RF signals to produce digitalsignals, which are combined and then processed to recapture thetransmitted data.

For a multiple-input-single-output (MISO) wireless communication, thetransmitter includes two or more transmission paths (e.g., digital toanalog converter, filters, up-conversion module, and a power amplifier)that each converts a corresponding portion of baseband signals into RFsignals, which are transmitted via corresponding antennas to a receiver.The receiver includes a single receiver path that receives the multipleRF signals from the transmitter. In this instance, the receiver usesbeam forming to combine the multiple RF signals into one signal forprocessing.

For a multiple-input-multiple-output (MIMO) wireless communication, thetransmitter and receiver each include multiple paths. In such acommunication, the transmitter parallel processes data using a spatialand time encoding function to produce two or more streams of data. Thetransmitter includes multiple transmission paths to convert each streamof data into multiple RF signals. The receiver receives the multiple RFsignals via multiple receiver paths that recapture the streams of datautilizing a spatial and time decoding function. The recaptured streamsof data are combined and subsequently processed to recover the originaldata.

To further improve wireless communications, transceivers may incorporatebeamforming. In general, beamforming is a processing technique to createa focused antenna beam by shifting a signal in time or in phase toprovide gain of the signal in a desired direction and to attenuate thesignal in other directions. Prior art papers (1) Digital beamformingbasics (antennas) by Steyskal, Hans, Journal of Electronic Defense, Jul.1, 1996; (2) Utilizing Digital Downconverters for Efficient DigitalBeamforming, by Clint Schreiner, Red River Engineering, no publicationdate; and (3) Interpolation Based Transmit Beamforming for MIMO-OFMDwith Partial Feedback, by Jihoon Choi and Robert W. Heath, University ofTexas, Department of Electrical and Computer Engineering, WirelessNetworking and Communications Group, Sep. 13, 2003 discuss beamformingconcepts.

In order for a transmitter to properly implement beamforming (i.e.,determine the beamforming matrix[V]), it needs to know properties of thechannel over which the wireless communication is conveyed. Accordingly,the receiver must provide feedback information for the transmitter todetermine the properties of the channel. One approach for sendingfeedback from the receiver to the transmitter is for the receiver todetermine the channel response (H) and to provide it as the feedbackinformation. An issue with this approach is the size of the feedbackpacket, which may be so large that, during the time it takes to send itto the transmitter, the response of the channel has changed.

To reduce the size of the feedback, the receiver may decompose thechannel using singular value decomposition (SVD) and send informationrelating only to a calculated value of the transmitter's beamformingmatrix (V) as the feedback information. In this approach, the receivercalculates (V) based on H=UDV*, where H is the channel response, D is adiagonal matrix, and U is a receiver unitary matrix. While this approachreduces the size of the feedback information, its size is still an issuefor a MIMO wireless communication. For instance, in a 2×2 MIMO wirelesscommunication, the feedback needs four elements that are all complexCartesian coordinate values[V11 V12; V21 V22]. In general,Vik=aik+j*bik, where aik and bik are values between [−1, 1]. Thus, with1 bit express per each element for each of the real and imaginarycomponents, aik and bik can be either −½ or ½, which requires 4×2×1=8bits per tone. With 4 bit expressions per each element of V(f) in anorthogonal frequency division multiplexing (OFDM) 2×2 MIMO wirelesscommunication, the number of bits required is 1728 per tone (e.g.,4*2*54*4=1728, 4 elements per tone, 2 bits for real and imaginarycomponents per tone, 54 data tones per frame, and 4 bits per element),which requires overhead for a packet exchange that is too large forpractical applications.

Therefore, a need exists for a method and apparatus for reducingbeamforming feedback information for wireless communications.

BRIEF SUMMARY OF THE INVENTION

The present invention is directed to apparatus and methods of operationthat are further described in the following Brief Description of theDrawings, the Detailed Description of the Invention, and the claims.Other features and advantages of the present invention will becomeapparent from the following detailed description of the invention madewith reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 is a schematic block diagram of a wireless communication systemin accordance with the present invention;

FIG. 2 is a schematic block diagram of a wireless communication devicein accordance with the present invention;

FIG. 3 is a schematic block diagram of another wireless communicationdevice in accordance with the present invention;

FIG. 4 is a schematic block diagram of baseband transmit processing inaccordance with the present invention;

FIG. 5 is a schematic block diagram of baseband receive processing inaccordance with the present invention; and

FIG. 6 is a schematic block diagram of a beamforming wirelesscommunication in accordance with the present invention.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 is a schematic block diagram illustrating a communication system10 that includes a plurality of base stations and/or access points 12,16, a plurality of wireless communication devices 18-32 and a networkhardware component 34. Note that the network hardware 34, which may be arouter, switch, bridge, modem, system controller, et cetera provides awide area network connection 42 for the communication system 10. Furthernote that the wireless communication devices 18-32 may be laptop hostcomputers 18 and 26, personal digital assistant hosts 20 and 30,personal computer hosts 24 and 32 and/or cellular telephone hosts 22 and28. The details of the wireless communication devices will be describedin greater detail with reference to FIG. 2.

Wireless communication devices 22, 23, and 24 are located within anindependent basic service set (IBSS) area and communicate directly(i.e., point to point). In this configuration, these devices 22, 23, and24 may only communicate with each other. To communicate with otherwireless communication devices within the system 10 or to communicateoutside of the system 10, the devices 22, 23, and/or 24 need toaffiliate with one of the base stations or access points 12 or 16.

The base stations or access points 12, 16 are located within basicservice set (BSS) areas 11 and 13, respectively, and are operablycoupled to the network hardware 34 via local area network connections36, 38. Such a connection provides the base station or access point 1216 with connectivity to other devices within the system 10 and providesconnectivity to other networks via the WAN connection 42. To communicatewith the wireless communication devices within its BSS 11 or 13, each ofthe base stations or access points 12-16 has an associated antenna orantenna array. For instance, base station or access point 12 wirelesslycommunicates with wireless communication devices 18 and 20 while basestation or access point 16 wirelessly communicates with wirelesscommunication devices 26-32. Typically, the wireless communicationdevices register with a particular base station or access point 12, 16to receive services from the communication system 10.

Typically, base stations are used for cellular telephone systems andlike-type systems, while access points are used for in-home orin-building wireless networks (e.g., IEEE 802.11 and versions thereof,Bluetooth, and/or any other type of radio frequency based networkprotocol). Regardless of the particular type of communication system,each wireless communication device includes a built-in radio and/or iscoupled to a radio.

FIG. 2 is a schematic block diagram illustrating a wirelesscommunication device that includes the host device 18-32 and anassociated radio 60. For cellular telephone hosts, the radio 60 is abuilt-in component. For personal digital assistants hosts, laptop hosts,and/or personal computer hosts, the radio 60 may be built-in or anexternally coupled component.

As illustrated, the host device 18-32 includes a processing module 50,memory 52, a radio interface 54, an input interface 58, and an outputinterface 56. The processing module 50 and memory 52 execute thecorresponding instructions that are typically done by the host device.For example, for a cellular telephone host device, the processing module50 performs the corresponding communication functions in accordance witha particular cellular telephone standard.

The radio interface 54 allows data to be received from and sent to theradio 60. For data received from the radio 60 (e.g., inbound data), theradio interface 54 provides the data to the processing module 50 forfurther processing and/or routing to the output interface 56. The outputinterface 56 provides connectivity to an output display device such as adisplay, monitor, speakers, et cetera such that the received data may bedisplayed. The radio interface 54 also provides data from the processingmodule 50 to the radio 60. The processing module 50 may receive theoutbound data from an input device such as a keyboard, keypad,microphone, et cetera via the input interface 58 or generate the dataitself. For data received via the input interface 58, the processingmodule 50 may perform a corresponding host function on the data and/orroute it to the radio 60 via the radio interface 54.

Radio 60 includes a host interface 62, digital receiver processingmodule 64, an analog-to-digital converter 66, a high pass and low passfilter module 68, an IF mixing down conversion stage 70, a receiverfilter 71, a low noise amplifier 72, a transmitter/receiver switch 73, alocal oscillation module 74, memory 75, a digital transmitter processingmodule 76, a digital-to-analog converter 78, a filtering/gain module 80,an IF mixing up conversion stage 82, a power amplifier 84, a transmitterfilter module 85, a channel bandwidth adjust module 87, and an antenna86. The antenna 86 may be a single antenna that is shared by thetransmit and receive paths as regulated by the Tx/Rx switch 73, or mayinclude separate antennas for the transmit path and receive path. Theantenna implementation will depend on the particular standard to whichthe wireless communication device is compliant.

The digital receiver processing module 64 and the digital transmitterprocessing module 76, in combination with operational instructionsstored in memory 75, execute digital receiver functions and digitaltransmitter functions, respectively. The digital receiver functionsinclude, but are not limited to, digital intermediate frequency tobaseband conversion, demodulation, constellation demapping, decoding,and/or descrambling. The digital transmitter functions include, but arenot limited to, scrambling, encoding, constellation mapping, modulation,and/or digital baseband to IF conversion. The digital receiver andtransmitter processing modules 64 and 76 may be implemented using ashared processing device, individual processing devices, or a pluralityof processing devices. Such a processing device may be a microprocessor,micro-controller, digital signal processor, microcomputer, centralprocessing unit, field programmable gate array, programmable logicdevice, state machine, logic circuitry, analog circuitry, digitalcircuitry, and/or any device that manipulates signals (analog and/ordigital) based on operational instructions. The memory 75 may be asingle memory device or a plurality of memory devices. Such a memorydevice may be a read-only memory, random access memory, volatile memory,non-volatile memory, static memory, dynamic memory, flash memory, and/orany device that stores digital information. Note that when theprocessing module 64 and/or 76 implements one or more of its functionsvia a state machine, analog circuitry, digital circuitry, and/or logiccircuitry, the memory storing the corresponding operational instructionsis embedded with the circuitry comprising the state machine, analogcircuitry, digital circuitry, and/or logic circuitry.

In operation, the radio 60 receives outbound data 94 from the hostdevice via the host interface 62. The host interface 62 routes theoutbound data 94 to the digital transmitter processing module 76, whichprocesses the outbound data 94 in accordance with a particular wirelesscommunication standard (e.g., IEEE 802.11, Bluetooth, et cetera) toproduce outbound baseband signals 96. The outbound baseband signals 96will be digital base-band signals (e.g., have a zero IF) or a digitallow IF signals, where the low IF typically will be in the frequencyrange of one hundred kilohertz to a few megahertz.

The digital-to-analog converter 78 converts the outbound basebandsignals 96 from the digital domain to the analog domain. Thefiltering/gain module 80 filters and/or adjusts the gain of the analogsignals prior to providing it to the IF mixing stage 82. The IF mixingstage 82 converts the analog baseband or low IF signals into RF signalsbased on a transmitter local oscillation 83 provided by localoscillation module 74. The power amplifier 84 amplifies the RF signalsto produce outbound RF signals 98, which are filtered by the transmitterfilter module 85. The antenna 86 transmits the outbound RF signals 98 toa targeted device such as a base station, an access point and/or anotherwireless communication device.

The radio 60 also receives inbound RF signals 88 via the antenna 86,which were transmitted by a base station, an access point, or anotherwireless communication device. The antenna 86 provides the inbound RFsignals 88 to the receiver filter module 71 via the Tx/Rx switch 73,where the Rx filter 71 bandpass filters the inbound RF signals 88. TheRx filter 71 provides the filtered RF signals to low noise amplifier 72,which amplifies the signals 88 to produce an amplified inbound RFsignals. The low noise amplifier 72 provides the amplified inbound RFsignals to the IF mixing module 70, which directly converts theamplified inbound RF signals into an inbound low IF signals or basebandsignals based on a receiver local oscillation 81 provided by localoscillation module 74. The down conversion module 70 provides theinbound low IF signals or baseband signals to the filtering/gain module68. The high pass and low pass filter module 68 filters, based onsettings provided by the channel bandwidth adjust module 87, the inboundlow IF signals or the inbound baseband signals to produce filteredinbound signals.

The analog-to-digital converter 66 converts the filtered inbound signalsfrom the analog domain to the digital domain to produce inbound basebandsignals 90, where the inbound baseband signals 90 will be digitalbase-band signals or digital low IF signals, where the low IF typicallywill be in the frequency range of one hundred kilohertz to a fewmegahertz. The digital receiver processing module 64, based on settingsprovided by the channel bandwidth adjust module 87, decodes,descrambles, demaps, and/or demodulates the inbound baseband signals 90to recapture inbound data 92 in accordance with the particular wirelesscommunication standard being implemented by radio 60. The host interface62 provides the recaptured inbound data 92 to the host device 18-32 viathe radio interface 54.

As one of average skill in the art will appreciate, the wirelesscommunication device of FIG. 2 may be implemented using one or moreintegrated circuits. For example, the host device may be implemented onone integrated circuit, the digital receiver processing module 64, thedigital transmitter processing module 76 and memory 75 may beimplemented on a second integrated circuit, and the remaining componentsof the radio 60, less the antenna 86, may be implemented on a thirdintegrated circuit. As an alternate example, the radio 60 may beimplemented on a single integrated circuit. As yet another example, theprocessing module 50 of the host device and the digital receiver andtransmitter processing modules 64 and 76 may be a common processingdevice implemented on a single integrated circuit. Further, the memory52 and memory 75 may be implemented on a single integrated circuitand/or on the same integrated circuit as the common processing modulesof processing module 50 and the digital receiver and transmitterprocessing module 64 and 76.

FIG. 3 is a schematic block diagram illustrating a wirelesscommunication device that includes the host device 18-32 and anassociated radio 60. For cellular telephone hosts, the radio 60 is abuilt-in component. For personal digital assistants hosts, laptop hosts,and/or personal computer hosts, the radio 60 may be built-in or anexternally coupled component.

As illustrated, the host device 18-32 includes a processing module 50,memory 52, radio interface 54, input interface 58 and output interface56. The processing module 50 and memory 52 execute the correspondinginstructions that are typically done by the host device. For example,for a cellular telephone host device, the processing module 50 performsthe corresponding communication functions in accordance with aparticular cellular telephone standard.

The radio interface 54 allows data to be received from and sent to theradio 60. For data received from the radio 60 (e.g., inbound data), theradio interface 54 provides the data to the processing module 50 forfurther processing and/or routing to the output interface 56. The outputinterface 56 provides connectivity to an output display device such as adisplay, monitor, speakers, et cetera such that the received data may bedisplayed. The radio interface 54 also provides data from the processingmodule 50 to the radio 60. The processing module 50 may receive theoutbound data from an input device such as a keyboard, keypad,microphone, et cetera via the input interface 58 or generate the dataitself For data received via the input interface 58, the processingmodule 50 may perform a corresponding host function on the data and/orroute it to the radio 60 via the radio interface 54.

Radio 60 includes a host interface 62, a baseband processing module 100,memory 65, a plurality of radio frequency (RF) transmitters 106-110, atransmit/receive (T/R) module 114, a plurality of antennas 81-85, aplurality of RF receivers 118-120, a channel bandwidth adjust module 87,and a local oscillation module 74. The baseband processing module 100,in combination with operational instructions stored in memory 65,executes digital receiver functions and digital transmitter functions,respectively. The digital receiver functions include, but are notlimited to, digital intermediate frequency to baseband conversion,demodulation, constellation demapping, decoding, de-interleaving, fastFourier transform, cyclic prefix removal, space and time decoding,and/or descrambling. The digital transmitter functions include, but arenot limited to, scrambling, encoding, interleaving, constellationmapping, modulation, inverse fast Fourier transform, cyclic prefixaddition, space and time encoding, and digital baseband to IFconversion. The baseband processing modules 100 may be implemented usingone or more processing devices. Such a processing device may be amicroprocessor, micro-controller, digital signal processor,microcomputer, central processing unit, field programmable gate array,programmable logic device, state machine, logic circuitry, analogcircuitry, digital circuitry, and/or any device that manipulates signals(analog and/or digital) based on operational instructions. The memory 65may be a single memory device or a plurality of memory devices. Such amemory device may be a read-only memory, random access memory, volatilememory, non-volatile memory, static memory, dynamic memory, flashmemory, and/or any device that stores digital information. Note thatwhen the processing module 100 implements one or more of its functionsvia a state machine, analog circuitry, digital circuitry, and/or logiccircuitry, the memory storing the corresponding operational instructionsis embedded with the circuitry comprising the state machine, analogcircuitry, digital circuitry, and/or logic circuitry.

In operation, the radio 60 receives outbound data 94 from the hostdevice via the host interface 62. The baseband processing module 64receives the outbound data 88 and, based on a mode selection signal 102,produces one or more outbound symbol streams 90. The mode selectionsignal 102 will indicate a particular mode of operation that iscompliant with one or more specific modes of the various IEEE 802.11standards. For example, the mode selection signal 102 may indicate afrequency band of 2.4 GHz, a channel bandwidth of 20 or 22 MHz and amaximum bit rate of 54 megabits-per-second. In this general category,the mode selection signal will further indicate a particular rateranging from 1 megabit-per-second to 54 megabits-per-second. Inaddition, the mode selection signal will indicate a particular type ofmodulation, which includes, but is not limited to, Barker CodeModulation, BPSK, QPSK, CCK, 16 QAM and/or 64 QAM. The mode selectsignal 102 may also include a code rate, a number of coded bits persubcarrier (NBPSC), coded bits per OFDM symbol (NCBPS), and/or data bitsper OFDM symbol (NDBPS). The mode selection signal 102 may also indicatea particular channelization for the corresponding mode that provides achannel number and corresponding center frequency. The mode selectsignal 102 may further indicate a power spectral density mask value anda number of antennas to be initially used for a MIMO communication.

The baseband processing module 100, based on the mode selection signal102 produces one or more outbound symbol streams 104 from the outbounddata 94. For example, if the mode selection signal 102 indicates that asingle transmit antenna is being utilized for the particular mode thathas been selected, the baseband processing module 100 will produce asingle outbound symbol stream 104. Alternatively, if the mode selectsignal 102 indicates 2, 3 or 4 antennas, the baseband processing module100 will produce 2, 3 or 4 outbound symbol streams 104 from the outbounddata 94.

Depending on the number of outbound streams 104 produced by the basebandmodule 10, a corresponding number of the RF transmitters 106-110 will beenabled to convert the outbound symbol streams 104 into outbound RFsignals 112. In general, each of the RF transmitters 106-110 includes adigital filter and upsampling module, a digital to analog conversionmodule, an analog filter module, a frequency up conversion module, apower amplifier, and a radio frequency bandpass filter. The RFtransmitters 106-110 provide the outbound RF signals 112 to thetransmit/receive module 114, which provides each outbound RF signal to acorresponding antenna 81-85.

When the radio 60 is in the receive mode, the transmit/receive module114 receives one or more inbound RF signals 116 via the antennas 81-85and provides them to one or more RF receivers 118-122. The RF receiver118-122, based on settings provided by the channel bandwidth adjustmodule 87, converts the inbound RF signals 116 into a correspondingnumber of inbound symbol streams 124. The number of inbound symbolstreams 124 will correspond to the particular mode in which the data wasreceived. The baseband processing module 100 converts the inbound symbolstreams 124 into inbound data 92, which is provided to the host device18-32 via the host interface 62.

As one of average skill in the art will appreciate, the wirelesscommunication device of FIG. 3 may be implemented using one or moreintegrated circuits. For example, the host device may be implemented onone integrated circuit, the baseband processing module 100 and memory 65may be implemented on a second integrated circuit, and the remainingcomponents of the radio 60, less the antennas 81-85, may be implementedon a third integrated circuit. As an alternate example, the radio 60 maybe implemented on a single integrated circuit. As yet another example,the processing module 50 of the host device and the baseband processingmodule 100 may be a common processing device implemented on a singleintegrated circuit. Further, the memory 52 and memory 65 may beimplemented on a single integrated circuit and/or on the same integratedcircuit as the common processing modules of processing module 50 and thebaseband processing module 100.

FIG. 4 is a schematic block diagram of baseband transmit processing100-TX within the baseband processing module 100, which includes anencoding module 121, a puncture module 123, a switch, a plurality ofinterleaving modules 125, 126, a plurality of constellation encodingmodules 128, 130, a beamforming module (V) 132, and a plurality ofinverse fast Fourier transform (IFFT) modules 134, 136 for convertingthe outbound data 94 into the outbound symbol stream 104. As one ofordinary skill in the art will appreciate, the baseband transmitprocessing may include two or more of each of the interleaving modules125, 126, the constellation mapping modules 128, 130, and the IFFTmodules 134, 136. In addition, one of ordinary skill in art will furtherappreciate that the encoding module 121, puncture module 123, theinterleaving modules 124, 126, the constellation mapping modules 128,130, and the IFFT modules 134, 136 may be function in accordance withone or more wireless communication standards including, but not limitedto, IEEE 802.11a, b, g, n.

In one embodiment, the encoding module 121 is operably coupled toconvert outbound data 94 into encoded data in accordance with one ormore wireless communication standards. The puncture module 123 puncturesthe encoded data to produce punctured encoded data. The plurality ofinterleaving modules 125, 126 is operably coupled to interleave thepunctured encoded data into a plurality of interleaved streams of data.The plurality of constellation mapping modules 128, 130 is operablycoupled to map the plurality of interleaved streams of data into aplurality of streams of data symbols. The beamforming module 132 isoperably coupled to beamform, using a unitary matrix having polarcoordinates, the plurality of streams of data symbols into a pluralityof streams of beamformed symbols. The plurality of IFFT modules 134, 136is operably coupled to convert the plurality of streams of beamformedsymbols into a plurality of outbound symbol streams.

The beamforming module 132 is operably coupled to multiply a beamformingunitary matrix (V) with baseband signals provided by the plurality ofconstellation mapping modules 128, 130. The beamforming module 132determines the beamforming unitary matrix V from feedback informationfrom the receiver, wherein the feedback information includes acalculated expression of the beamforming matrix V having polarcoordinates. The beamforming module 132 generates the beamformingunitary matrix V to satisfy the conditions of “V*V=VV*=“I”, where “I” isan identity matrix of [1 0; 0 1] for 2×2 MIMO wireless communication, is[1 0 0; 0 1 0; 0 0 1] for 3×3 MIMO wireless communication, or is [1 0 00; 0 1 0 0; 0 0 1 0; 0 0 0 1] for 4×4 MIMO wireless communication. Inthis equation, V*V means “conjugate (V) times V” and VV* means “V timesconjugate (V)”. Note that V may be a 2×2 unitary matrix for a 2×2 MIMOwireless communication, a 3×3 unitary matrix for a 3×3 MIMO wirelesscommunication, and a 4×4 unitary matrix for a 4×4 MIMO wirelesscommunication. Further note that for each column of V, a first row ofpolar coordinates including real values as references and a second rowof polar coordinates including phase shift values.

In one embodiment, the constellation mapping modules 128, 130 functionin accordance with one of the IEEE 802.11x standards to provide an OFDM(Orthogonal Frequency Domain Multiplexing) frequency domain basebandsignals that includes a plurality of tones, or subcarriers, for carryingdata. Each of the data carrying tones represents a symbol mapped to apoint on a modulation dependent constellation map. For instance, a 16QAM (Quadrature Amplitude Modulation) includes 16 constellation points,each corresponding to a different symbol. For an OFDM signal, thebeamforming module 132 may regenerate the beamforming unitary matrix Vfor each tone from each constellation mapping module 128, 130, use thesame beamforming unitary matrix for each tone from each constellationmapping module 128, 130, or a combination thereof.

The beamforming unitary matrix varies depending on the number oftransmit paths (i.e., transmit antennas−M) and the number of receivepaths (i.e., receiver antennas−N) for an M×N MIMO communication. Forinstance, for a 2×2 MIMO communication, the beamforming unitary matrixmay be:

$V = \begin{bmatrix}{\cos\;\psi_{1}} & {\cos\;\psi_{2}} \\{\sin\;\psi_{1}{\mathbb{e}}^{j\;\phi_{1}}} & {\sin\;\psi_{2}{\mathbb{e}}^{j\;\phi_{2}}}\end{bmatrix}$In order to satisfy V*V=I, it needs to satisfy followings.cos ψ₁ cos ψ₂+sin ψ₁ sin ψ₂ e ^(j(φ) ¹ ^(−φ) ² ⁾=0cos ψ₁ cos ψ₂+sin ψ₁ sin ψ₂ e ^(j(φ) ² ^(−φ) ¹ ⁾=0where i, j=1, 2; ψ₁, Φ₁, ψ₂, and Φ₂ represent angles of the unit circle,wherein absolute value of ψ₁−ψ₂=π/2 and Φ₁=Φ₂ or Φ₁=ψ₂+π and ψ₁+ψ₂=π/2.

Therefore, with Φ₁ and ψ₁, the beamforming module 132 may regenerate Vper each tone. For example, With 4-bits expression for angle Φ₁ and3-bits for angle ψ₁, and 1-bit for the index for #1 or #2 in 54 tones,(i.e., 8-bits per tone) total feedback information may be 8×54/8=54bytes. (ψ in [0, π], Φ in [−π, π]).

For a 3×3 MIMO communication, the beamforming unitary matrix may be:

$V = {{(V){ij}} = \begin{bmatrix}{\cos\;\psi_{1}} & {\cos\;\psi_{2}} & {\cos\;\psi_{3}} \\{\sin\;\psi_{1}\cos\;\theta_{1}{\mathbb{e}}^{j\;\phi_{21}}} & {\sin\;\psi_{2}\cos\;\theta_{2}{\mathbb{e}}^{j\;\phi_{22}}} & {\sin\;\psi_{3}\cos\;\theta_{3}{\mathbb{e}}^{j\;\phi_{23}}} \\{\sin\;\psi_{1}\sin\;\theta_{1}{\mathbb{e}}^{j\;\phi_{31}}} & {\sin\;\psi_{2}\sin\;\theta_{2}{\mathbb{e}}^{j\;\phi_{32}}} & {\sin\;\psi_{3}\sin\;\theta_{3}{\mathbb{e}}^{j\;\phi_{33}}}\end{bmatrix}}$where i, j=1, 2, 3; ψ₁, ψ₂, ψ₃, θ₁, θ₂, θ₃, Φ₂₁, Φ₂₂, Φ₂₃, Φ₃₁, Φ₃₂, Φ₃₃represent angles of the unit circle, wherein Diagonal (V*V)=1 s, andwherein:

${\psi_{i} = {\cos^{- 1}V_{1i}}},{\theta_{i} = {\cos^{- 1}{\frac{V_{2i}}{\sin\;\psi_{i}}}}}$ϕ_(2i) = ∠(V_(2i)), ϕ_(3i) = ∠(V_(3i))

In this example, with 12 angles, the beamforming module 132 mayregenerate V as a 3×3 matrix per tone. With 4-bits for expression forthe angles, a 54 tone signal may have feedback information of 324 bytes(e.g., 4×12×54/8).

For a 4×4 MIMO communication, the beamforming unitary matrix may be:

$V = {{(V){ij}} = \begin{bmatrix}{\cos\;\psi_{1}\cos\;\varphi_{1}} & {\cos\;\psi_{2}\cos\;\varphi_{2}} & {\cos\;\psi_{3}\cos\;\varphi_{3}} & {\cos\;\psi_{4}\cos\;\varphi_{4}} \\{\cos\;\psi_{1}\sin\;\varphi_{1}{\mathbb{e}}^{j\;\phi_{11}}} & {\cos\;\psi_{2}\sin\;\varphi_{2}{\mathbb{e}}^{j\;\phi_{12}}} & {\cos\;\psi_{3}\sin\;\varphi_{3}{\mathbb{e}}^{j\;\phi_{13}}} & {\cos\;\psi_{4}\sin\;\varphi_{4}{\mathbb{e}}^{j\;\phi_{14}}} \\{\sin\;\psi_{1}\cos\;\theta_{1}{\mathbb{e}}^{j\;\phi_{21}}} & {\sin\;\psi_{2}\cos\;\theta_{2}{\mathbb{e}}^{j\;\phi_{22}}} & {\sin\;\psi_{3}\cos\;\theta_{3}{\mathbb{e}}^{j\;\phi_{23}}} & {\sin\;\psi_{4}\cos\;\theta_{4}{\mathbb{e}}^{j\;\phi_{24}}} \\{\sin\;\psi_{1}\sin\;\theta_{1}{\mathbb{e}}^{j\;\phi_{31}}} & {\sin\;\psi_{2}\sin\;\theta_{2}{\mathbb{e}}^{j\;\phi_{32}}} & {\sin\;\psi_{3}\sin\;\theta_{3}{\mathbb{e}}^{j\;\phi_{33}}} & {\sin\;\psi_{4}\sin\;\theta_{4}{\mathbb{e}}^{j\;\phi_{34}}}\end{bmatrix}}$=[cos(ψ₁) cos(ψ₂); sin(ψ₁)*e^(jΦ1) sin(ψ₂)*e^(jΦ2)], where i, j=1, 2, 3,4; wherein ψ₁, ψ₂, ψ₃, ψ₄, θ₁, θ₂, θ₃, θ₄, Φ₁, Φ₂, Φ₃, Φ₄, Φ₂₁, Φ₂₂,Φ₂₃, Φ₂₄, Φ₃₁, Φ₃₂, Φ₃₃, Φ₃₃, Φ₄₁, Φ₄₂, Φ₄₃, Φ₄₃ represent angles of theunit circle, wherein Diagonal (V*V)=1 s, and wherein:

${\psi_{i} = {\cos^{- 1}\left( \sqrt{{V_{1i}}^{2} + {V_{2i}}^{2}} \right)}},{\varphi_{i} = {\cos^{- 1}\left( \frac{V_{1i}}{\cos\;\psi_{i}} \right)}},{\theta_{i} = {\cos^{- 1}{\frac{V_{3i}}{\sin\;\psi_{i}}}}}$ϕ_(1i) = ∠(V_(2i)), ϕ_(2i) = ∠(V_(3i)), ϕ_(3i) = ∠(V_(4i))

In this example, with 24 angles, the beamforming module 132 mayregenerate V as a 4×4 matrix per tone. With 4-bits for expression forthe angles, a 54 tone signal may have feedback information of 648 bytes(e.g., 4×24×54/8).

The baseband transmit processing 100-TX receives the polar coordinates Φand ψ from the receiver as feedback information as will described ingreater detail with reference to FIG. 6.

FIG. 5 is a schematic block diagram of baseband receive processing100-RX that includes a plurality of fast Fourier transform (FFT) modules140, 142, a beamforming (U) module 144, a plurality of constellationdemapping modules 146, 148, a plurality of deinterleaving modules 150,152, a switch, a depuncture module 154, and a decoding module 156 forconverting a plurality of inbound symbol streams 124 into inbound data92. As one of ordinary skill in the art will appreciate, the basebandreceive processing 100-RX may include two or more of each of thedeinterleaving modules 150, 152, the constellation demapping modules146, 148, and the FFT modules 140, 142. In addition, one of ordinaryskill in art will further appreciate that the decoding module 156,depuncture module 154, the deinterleaving modules 150, 152, theconstellation decoding modules 146, 148, and the FFT modules 140, 142may be function in accordance with one or more wireless communicationstandards including, but not limited to, IEEE 802.11a, b, g, n.

In one embodiment, a plurality of FFT modules 140, 142 is operablycoupled to convert a plurality of inbound symbol streams 124 into aplurality of streams of beamformed symbols. The inverse beamformingmodule 144 is operably coupled to inverse beamform, using a unitarymatrix having polar coordinates, the plurality of streams of beamformedsymbols into a plurality of streams of data symbols. The plurality ofconstellation demapping modules is operably coupled to demap theplurality of streams of data symbols into a plurality of interleavedstreams of data. The plurality of deinterleaving modules is operablycoupled to deinterleave the plurality of interleaved streams of datainto encoded data. The decoding module is operably coupled to convertthe encoded data into inbound data 92.

The beamforming module 144 is operably coupled to multiply a beamformingunitary matrix (U) with baseband signals provided by the plurality ofFFT modules 140, 142. The FFT modules 140, 142 function in accordancewith one of the IEEE 802.11x standards to provide an OFDM (OrthogonalFrequency Domain Multiplexing) frequency domain baseband signals thatincludes a plurality of tones, or subcarriers, for carrying data. Eachof the data carrying tones represents a symbol mapped to a point on amodulation dependent constellation map. The baseband receive processing100-RX is further functional to produce feedback information for thetransmitter as further described with reference to FIG. 6.

FIG. 6 is a schematic block diagram of a beamforming wirelesscommunication where H=UDV* (H—represents the channel, U is the receiverbeamforming unitary matrix, and V* is the conjugate of the transmitterbeamforming unitary matrix. With H=UDV*, y (the received signal)=Hx+N,where x represents the transmitted signals and N represents noise. Ifz=Vx, then U*y=U*UDV*VZ+U*n=Dz+N.

From this expression, the baseband receive processing 100-RX may readilydetermine the feedback of V, where V includes polar coordinates. Forinstance, the receiver may decompose the channel using singular valuedecomposition (SVD) and send information relating only to a calculatedvalue of the transmitter's beamforming matrix (V) as the feedbackinformation. In this approach, the receiver calculates (V) based onH=UDV*, where H is the channel response, D is a diagonal matrix, and Uis a receiver unitary matrix. This approach reduces the size of thefeedback information with respect to SVD using Cartesian coordinates.For example, in a 2×2 MIMO wireless communication, the feedback needsfour elements that are all complex values [V11 V12; V21 V22] with twoangles (ψ and Φ). In general, Vik=aik+j*bik, where aik and bik arevalues between [−1, 1]. To cover [−1, 1], ψ is in [0, π] and Φ is in [0,2π]. With π/2 resolutions for angles, ψ needs to be π/4 or 3π/4, i.e.,cos(ψ)=0.707 or −0.707, which requires 1 bit, where Φ needs to be eitherπ/4, 3π/4, 5π/4, 7π/4, i.e., exp(jΦ)=0.707(1+j), 0.707(1−j), 0.707(−1+j)or 0.707(−1−j), which requires 2 bits. With π/4 resolutions for angles,ψ needs to be π/8, 3π/8, 5π/8 or 7π/8, which requires 2 bits, where Φneeds to be either π/8, 3π/8, 5π/8, 7π/8, 9π/8, 11π/8, 13π/8 or 15π/8,which requires 4 bits. So, for an example of 2×2 system to use 4 bitsper tone, it may have 1 bit for ψ, 2 bits for Φ and 1 index bit todetermine the relationship between ψ and Φ, such as either ψ1=ψ2+π andΦ1+Φ2=π/2, or ψ1=ψ2 and Φ1−ψ2=π/2.

For the same resolution in Cartesian expression of 4 bits per eachelement for each of the real and imaginary components, aik and bik, canbe within [−½, ½], it requires 4*2*4=32 bits per tone. For OFDM MIMOwireless communications, the number of bits required is 1728 bits forthe Cartesian expression. While an angle expression in accordance withthe present invention requires 8 bits per tone, which for the same OFDMMIMO wireless communications would require 432 bits. This represents asignificant reduction in the overhead needed for packet exchange.

The preceding discussion has presented a method and apparatus forreducing feedback information for beamforming in a wirelesscommunication by using polar coordinates. As one of average skill in theart will appreciate, other embodiments may be derived from the presentteachings without deviating from the scope of the claims.

1. A method for reduced feedback for beamforming in a wirelesscommunication, the method comprises: receiving a baseband signal by atransmitter that includes a plurality of streams; determining a unitarymatrix V by the transmitter in response to feedback information receivedfrom a receiver, wherein the feedback information for a 2×N unitarymatrix V, wherein N is a number of receiver antennas, includes angles ofa unit circle ψ₁, Φ₁ and an index bit that defines a relationshipbetween ψ₁ and Φ₁ and wherein determining the 2×N unitary matrixincludes: determining the set of angles ψ₁ and Φ₁, ψ₂, and Φ₂ inresponse to the feedback information; determining a plurality of polarcoordinates represented by the 2×N unitary matrix V based on the set ofangles ψ₁ and Φ₁, ψ₂, Φ₂, wherein absolute value of each of theplurality of polar coordinates is a vector on a unit circle and each ofthe polar coordinates is orthogonal to at least one other of the polarcoordinates such that VV*=V*V=I, where I represents an identity matrix;and for each column of V, a first row of polar coordinates includes realvalues as references and a second row of polar coordinates includesphase shift values; and digitally beamforming each of the plurality ofstreams of the baseband signal using the unitary matrix to produce aplurality of beamformed symbols.
 2. The method of claim 1 comprises: thebaseband signal including a plurality of tones, wherein each of theplurality of tones corresponds to a symbol mapped to a constellation;and digital beamforming each of the plurality of tones using the unitarymatrix.
 3. The method of claim 1 comprises: receiving outbound data;encoding the outbound data to produce a stream of encoded data;interleaving the stream of encoded data into a plurality of parallelstreams of interleaved data; constellation mapping symbols of each ofthe plurality of parallel streams of interleaved data to a plurality ofparallel tones; and digital beamforming each of the plurality ofparallel tones using the unitary matrix.
 4. The method of claim 1,wherein the 2×N unitary matrix comprises for a 2×N multiple inputmultiple output (MIMO) wireless communication: $V = \begin{bmatrix}{\cos\;\psi_{1}} & {\cos\;\psi_{2}} \\{\sin\;\psi_{1}{\mathbb{e}}^{j\;\phi_{1}}} & {\sin\;\psi_{2}{\mathbb{e}}^{j\;\phi_{2}}}\end{bmatrix}$ wherein ψ₁, Φ₁, ψ₂, and Φ₂ represent angles of the unitcircle, wherein absolute value of ψ₁−ψ₂=π/2 and Φ₁=Φ₂ or Φ₁=Φ₂+π andψ₁+ψ₂=/2; and wherein the index bit in the feedback information defineswhether ψ₁−ψ₂=π/2 and Φ₁=Φ₂ or Φ₁=Φ₂+π and ψ₁+ψ₂=π/2.
 5. The method ofclaim 1, wherein the unitary matrix further comprises for a 3×N multipleinput multiple output (MIMO) wireless communication:$V = \begin{bmatrix}{\cos\;\psi_{1}} & {\cos\;\psi_{2}} & {\cos\;\psi_{3}} \\{\sin\;\psi_{1}\cos\;\theta_{1}{\mathbb{e}}^{j\;\phi_{21}}} & {\sin\;\psi_{2}\cos\;\theta_{2}{\mathbb{e}}^{j\;\phi_{22}}} & {\sin\;\psi_{3}\cos\;\theta_{3}{\mathbb{e}}^{j\;\phi_{23}}} \\{\sin\;\psi_{1}\sin\;\theta_{1}{\mathbb{e}}^{j\;\phi_{31}}} & {\sin\;\psi_{2}\sin\;\theta_{2}{\mathbb{e}}^{j\;\phi_{32}}} & {\sin\;\psi_{3}\sin\;\theta_{3}{\mathbb{e}}^{j\;\phi_{33}}}\end{bmatrix}$ wherein ψ₁, ψ₂, ψ₃, θ₁, θ₂, θ₃, Φ₂₁, Φ₂₂, Φ₂₃, Φ₃₁, Φ₃₂,Φ₃₃ represent angles of the unit circle, wherein Diagonal (V*V)=1 s, andwherein:${\psi_{i} = {\cos^{- 1}V_{1i}}},{\theta_{i} = {\cos^{- 1}{\frac{V_{2i}}{\sin\;\psi_{i}}}}}$ϕ_(2i) = ∠(V_(2i)), ϕ_(3i) = ∠(V_(3i)).
 6. The method of claim 1,wherein the unitary matrix further comprises for a 4×N multiple inputmultiple output (MIMO) wireless communication: $V = \begin{bmatrix}{\cos\;\psi_{1}\cos\;\varphi_{1}} & {\cos\;\psi_{2}\cos\;\varphi_{2}} & {\cos\;\psi_{3}\cos\;\varphi_{3}} & {\cos\;\psi_{4}\cos\;\varphi_{4}} \\{\cos\;\psi_{1}\sin\;\varphi_{1}{\mathbb{e}}^{j\;\phi_{11}}} & {\cos\;\psi_{2}\sin\;\varphi_{2}{\mathbb{e}}^{j\;\phi_{12}}} & {\cos\;\psi_{3}\sin\;\varphi_{3}{\mathbb{e}}^{j\;\phi_{13}}} & {\cos\;\psi_{4}\sin\;\varphi_{4}{\mathbb{e}}^{j\;\phi_{14}}} \\{\sin\;\psi_{1}\cos\;\theta_{1}{\mathbb{e}}^{j\;\phi_{21}}} & {\sin\;\psi_{2}\cos\;\theta_{2}{\mathbb{e}}^{j\;\phi_{22}}} & {\sin\;\psi_{3}\cos\;\theta_{3}{\mathbb{e}}^{j\;\phi_{23}}} & {\sin\;\psi_{4}\cos\;\theta_{4}{\mathbb{e}}^{j\;\phi_{24}}} \\{\sin\;\psi_{1}\sin\;\theta_{1}{\mathbb{e}}^{j\;\phi_{31}}} & {\sin\;\psi_{2}\sin\;\theta_{2}{\mathbb{e}}^{j\;\phi_{32}}} & {\sin\;\psi_{3}\sin\;\theta_{3}{\mathbb{e}}^{j\;\phi_{33}}} & {\sin\;\psi_{4}\sin\;\theta_{4}{\mathbb{e}}^{j\;\phi_{34}}}\end{bmatrix}$ wherein ψ₁, ψ₂, ψ₃, ψ₄, θ₁, θ₂, θ₃, θ₄, φ₁, φ₂, φ₃, φ₄,Φ₂₁, Φ₂₂, Φ₂₃, Φ₃₂, Φ₃₃, Φ₃₃, Φ₄₁, Φ₄₁, Φ₄₂, Φ₄₃ represent angles of theunit circle, wherein Diagonal (V*V)=1 s, and wherein:${\psi_{i} = {\cos^{- 1}\left( \sqrt{{V_{1i}}^{2} + {V_{2i}}^{2}} \right)}},{\varphi_{i} = {\cos^{- 1}\left( \frac{V_{1i}}{\cos\;\psi_{i}} \right)}},{\theta_{i} = {\cos^{- 1}{\frac{V_{3i}}{\sin\;\psi_{i}}}}}$ϕ_(1i) = ∠(V_(2i)), ϕ_(2i) = ∠(V_(3i)), ϕ_(3i) = ∠(V_(4i))
 7. A transmitbaseband processing module comprises: an encoding module operablycoupled to convert outbound data into encoded data; a plurality ofinterleaving modules operably coupled to interleave the encoded datainto a plurality of interleaved streams of data; a plurality ofconstellation mapping modules operably coupled to map the plurality ofinterleaved streams of data into a plurality of streams of data symbols;a beamforming module operably coupled to beamform, using a unitarymatrix, the plurality of streams of data symbols into a plurality ofstreams of beamformed symbols, wherein the unitary matrix is based onfeedback information from a receiver, wherein a 2×N unitary matrix V,wherein N is a number of receiver antennas, includes: a plurality ofpolar coordinates, wherein the plurality of polar coordinates aredetermined in response to the feedback information, wherein the feedbackinformation includes angles of a unit circle ψ₁, Φ₁ and an index bitthat defines a relationship between ψ₁ and Φ₁ and wherein absolute valueof each of the plurality of polar coordinates is a vector on a unitcircle and each of the polar coordinates is orthogonal to at least oneother of the polar coordinates such that VV*=V*V=I, where I representsan identity matrix; and for each column of V, a first row of polarcoordinates includes real values as references and a second row of polarcoordinates includes phase shift values; and a plurality of inverse fastFourier transform modules operably coupled to convert the plurality ofstreams of beamformed symbols into a plurality of outbound symbolstreams.
 8. The transmit baseband processing module of claim 7, whereinthe unitary matrix further comprises for a 2×N multiple input multipleoutput (MIMO) wireless communication: $V = \begin{bmatrix}{\cos\;\psi_{1}} & {\cos\;\psi_{2}} \\{\sin\;\psi_{1}{\mathbb{e}}^{j\;\phi_{1}}} & {\sin\;\psi_{2}{\mathbb{e}}^{j\;\phi_{2}}}\end{bmatrix}$ wherein ψ₁, Φ₁, ψ₂, and Φ₂ represent angles of the unitcircle, wherein absolute value of ψ₁−ψ₂=π/2 and Φ₁=Φ₂ or Φ₁=Φ₂+π andψ₁+ψ₂=π/2; and wherein the feedback information includes ψ₁, Φ₁ and anindex bit to determine the relationship between ψ₁ and Φ₁.
 9. Thetransmit baseband processing module of claim 7, wherein the unitarymatrix further comprises for a 3×N multiple input multiple output (MIMO)wireless communication: $V = \begin{bmatrix}{\cos\;\psi_{1}} & {\cos\;\psi_{2}} & {\cos\;\psi_{3}} \\{\sin\;\psi_{1}\cos\;\theta_{1}{\mathbb{e}}^{j\;\phi_{21}}} & {\sin\;\psi_{2}\cos\;\theta_{2}{\mathbb{e}}^{j\;\phi_{22}}} & {\sin\;\psi_{3}\cos\;\theta_{3}{\mathbb{e}}^{j\;\phi_{23}}} \\{\sin\;\psi_{1}\sin\;\theta_{1}{\mathbb{e}}^{j\;\phi_{31}}} & {\sin\;\psi_{2}\sin\;\theta_{2}{\mathbb{e}}^{j\;\phi_{32}}} & {\sin\;\psi_{3}\sin\;\theta_{3}{\mathbb{e}}^{j\;\phi_{33}}}\end{bmatrix}$ wherein ψ₁, ψ₂, ψ₃, θ₁, θ₂, θ₃, Φ₂₁, Φ₂₂, Φ₂₃, Φ₃₁, Φ₃₂,Φ₃₃ represent angles of the unit circle, wherein Diagonal (V*V)=1 s, andwherein: $\quad\begin{matrix}{{\psi_{i} = {\cos^{- 1}V_{1i}}},} \\{\theta_{i} = {\cos^{- 1}{\frac{V_{2i}}{\sin\;\psi_{i}}}}} \\{{\phi_{2i} = {\angle\left( V_{2i} \right)}},} \\{\phi_{3i} = {{\angle\left( V_{3i} \right)}.}}\end{matrix}$
 10. The transmit baseband processing module of claim 7,wherein the unitary matrix further comprises for a 4×N multiple inputmultiple output (MIMO) wireless communication: $V = \begin{bmatrix}{\cos\;\psi_{1}\cos\;\varphi_{1}} & {\cos\;\psi_{2}\cos\;\varphi_{2}} & {\cos\;\psi_{3}\cos\;\varphi_{3}} & {\cos\;\psi_{4}\cos\;\varphi_{4}} \\{\cos\;\psi_{1}\sin\;\varphi_{1}{\mathbb{e}}^{j\;\phi_{11}}} & {\cos\;\psi_{2}\sin\;\varphi_{2}{\mathbb{e}}^{j\;\phi_{12}}} & {\cos\;\psi_{3}\sin\;\varphi_{3}{\mathbb{e}}^{j\;\phi_{13}}} & {\cos\;\psi_{4}\sin\;\varphi_{4}{\mathbb{e}}^{j\;\phi_{14}}} \\{\sin\;\psi_{1}\cos\;\theta_{1}{\mathbb{e}}^{j\;\phi_{21}}} & {\sin\;\psi_{2}\cos\;\theta_{2}{\mathbb{e}}^{j\;\phi_{22}}} & {\sin\;\psi_{3}\cos\;\theta_{3}{\mathbb{e}}^{j\;\phi_{23}}} & {\sin\;\psi_{4}\cos\;\theta_{4}{\mathbb{e}}^{j\;\phi_{24}}} \\{\sin\;\psi_{1}\sin\;\theta_{1}{\mathbb{e}}^{j\;\phi_{31}}} & {\sin\;\psi_{2}\sin\;\theta_{2}{\mathbb{e}}^{j\;\phi_{32}}} & {\sin\;\psi_{3}\sin\;\theta_{3}{\mathbb{e}}^{j\;\phi_{33}}} & {\sin\;\psi_{4}\sin\;\theta_{4}{\mathbb{e}}^{j\;\phi_{34}}}\end{bmatrix}$ wherein ψ₁, ψ₂, ψ₃, ψ₄, θ₁, θ₂, θ₃, θ₄, φ₁, φ₂, φ₃, φ₄,Φ₂₁, Φ₂₂, Φ₂₃, Φ₂₄, Φ₃₁, Φ₃₂, Φ₃₃, Φ₃₃, Φ₄₁, Φ₄₂, Φ₄₃, Φ₄₃ representangles of the unit circle, wherein Diagonal (V*V)=1 s, and wherein:$\quad\begin{matrix}{{\psi_{i} = {\cos^{- 1}\left( \sqrt{{V_{1i}}^{2} + {V_{2i}}^{2}} \right)}},} \\{{\varphi_{i} = {\cos^{- 1}\left( \frac{V_{1i}}{\cos\;\psi_{i}} \right)}},} \\{\theta_{i} = {\cos^{- 1}{\frac{V_{3i}}{\sin\;\psi_{i}}}}} \\{{\phi_{1i} = {\angle\left( V_{2i} \right)}},} \\{{\phi_{2i} = {\angle\left( V_{3i} \right)}},} \\{\phi_{3i} = {\angle{\left( V_{4i} \right).}}}\end{matrix}$
 11. A receiver baseband processing module comprises: aplurality of fast Fourier transform modules operably coupled to converta plurality of inbound symbol streams into a plurality of streams ofbeamformed symbols; an inverse beamforming module operably coupled toinverse beamform, using a unitary matrix having polar coordinates, theplurality of streams of beamformed symbols into a plurality of streamsof data symbols, wherein the polar coordinates of the unitary matrix arebased on feedback information that includes angles of a unit circle ψ₁,Φ₁ and an index bit that defines a relationship between ψ₁ and Φ₁ andwherein the unitary matrix includes: a plurality of polar coordinatesrepresented by U, wherein the plurality of polar coordinates aredetermined in response to the feedback information and wherein absolutevalue of each of the plurality of polar coordinates is a vector on aunit circle and each of the polar coordinates is orthogonal to at leastone other of the polar coordinates UU*=U*U=I, where I represents anidentity matrix; and for each column of U, a first row of polarcoordinates includes real values as references and a second row of polarcoordinates includes phase shift values; a plurality of constellationdemapping modules operably coupled to demap the plurality of streams ofdata symbols into a plurality of interleaved streams of data; aplurality of deinterleaving modules operably coupled to deinterleave theplurality of interleaved streams of data into encoded data; and adecoding module operably coupled to convert the encoded data intoinbound data.